## Main

Pre-landing predictions based on modelling and on data from Mars Science Laboratory (Curiosity)’s entry, descent and landing (EDL) in 2012 suggested that the impact of the spacecraft’s two cruise balance mass devices (CBMDs, also referred to as cruise mass balance devices, or CMBDs) might produce seismic waves of high enough amplitude to be detectable at the position of InSight (Interior Exploration using Seismic Investigations, Geodesy and Heat Transport), approximately 3,450 km to the east6,7.

The CBMDs are solid, 77.5 kg tungsten blocks used to adjust the spacecraft’s lift-to-drag ratio during EDL. Data from the spacecraft’s computer indicate that the commands were generated to fire the pyrotechnic releases holding them in place at 20:28:27 utc, within 1 s of each other. At this time, the spacecraft was projected to be at an altitude of 1,253 km and travelling at a planet-relative velocity of 4,753 m s−1.

NASA’s trajectory reconstruction indicates that the CBMDs hit the surface at 20:40:33 ± 3 s utc (around five minutes before the rover’s touchdown), at a speed of approximately 3,816 m s−1 and an oblique angle of around 10° from the horizontal.

The impact craters from the CBMDs were imaged by the CTX (Context Camera)8 and HiRISE (High Resolution Imaging Science Experiment) instruments9 on board NASA’s Mars Reconnaissance Orbiter on 3 May 2021. Images identified the craters at a position around 18.9° N 76.2° E (Fig. 1).

The most promising candidate seismic phase for detection at InSight (4.5° N, 135.6° E) was expected to be a ballistic compressional (P) wave excited by the CBMD impact (Fig. 5 in ref. 7). The P-wave arrival time was predicted to be approximately 420 ± 20 s after impact, or 20:47 utc (19:50 InSight Local Mars Solar Time, lmst, on sol 793).

The two variables determining whether or not this signal would be identifiable in InSight data were the seismic noise during the arrival window (constrained after landing from the seismometer recordings), and the amplitude of the impact-induced P wave. The former was particularly low during the arrival window, as it occurred during the part of InSight’s day when the atmospheric noise is lowest. The latter was predicted using distance–amplitude scaling curves7,10,11. These relationships come with large uncertainties, as they are calibrated using only terrestrial and lunar data at closer range.

Data were recorded throughout the night (in utc) of 18–19 February 2021 on InSight’s Very Broad Band (VBB) seismometer12, and the pressure and wind sensors of the Auxiliary Payload Sensor Suite (APSS)13.

Data from the arrival window are plotted in Fig. 2. The main signals observed are a large marsquake around 01:25 utc, and irregularly spaced glitches, which are artificial in origin. No other signal is observed that cannot be explained as noise excited by atmospheric phenomena, as corroborated using the wind speed and pressure measurements.

Therefore, we conclude that no signal associated with the CBMD impact is identifiable above the detection threshold (as defined in Fig. 2b), precluding a P-wave amplitude larger than 1.1 × 10−10 m s−1.

As the marsquake detected at 01:25 utc fits within the projected time window (4–5 h after landing) for infrasound (low-frequency sound) waves to arrive from Perseverance’s EDL, we will briefly outline why we believe it is unrelated and simply coincidental.

This assessment is based on the signal’s amplitude, shape and frequency content, which are entirely different from those of an infrasound wave. EDL-related infrasounds at these distances should have amplitudes below the noise floor7, whilst the high frequencies observed in this event (up to ~30 Hz) preclude an airborne propagation path, as the high CO2 concentration in the Martian atmosphere would rapidly attenuate them14. Rather, this event (‘S0794a’) is a standard ‘very high-frequency’ marsquake15, in this case with an origin at a distance of ~1,100 km, much closer than Perseverance. As of the end of April 2021, 40 of these events have been recorded by InSight, often in the late evening16. These events are probably caused by tectonic or otherwise internal geological processes.

Having established that there is no signal from the EDL recorded in the data, we will now consider what this non-detection can be used to infer about impact processes on Mars.

There are a number of approaches to using distance–amplitude scaling relationships to predict peak P-wave amplitudes from impacts.

Depending on whether the impactor energy, total momentum or vertical component of the momentum is used to scale the amplitude, and whether terrestrial missile-impact data or lunar spacecraft-impact data are the basis, predicted amplitudes vary by up to two orders of magnitude when extrapolated to distances of 3,500 km. Five such standard scaling relationships are shown in Fig. 3—one based on impactor energy10, and four based on impactor momentum11.

Of the latter, two are based on data from artificial lunar impacts, which occurred into almost cohesionless material (black curves, ref. 5), and two on terrestrial missile impacts into weakly cohesive regolith soils (green curves, ref. 17). In each case, one curve uses the total impactor momentum as the determinant of peak P-wave amplitude (solid lines), whilst the other uses the vertical component of the impactor momentum (dashed lines).

The derived upper bound on the peak P-wave amplitude of 1.1 × 10−10 m s−1 is shown as a horizontal grey line in Fig. 3, and at the distance in question lies below the solid green scaling curve (total impactor momentum; terrestrial missile data).

This result indicates that the distance–amplitude scaling relationship based on terrestrial missile impacts into weakly cohesive soil, and the assumption that seismic wave amplitudes scale with total impactor momentum, are not appropriate in this case. There are three possible implications.

First, for highly oblique impacts such as this, this result suggests that the vertical component of the momentum may be a more appropriate quantity to scale by.

Alternatively, as the impact data on which this model was based were collected at much closer distances and on Earth, this may indicate a stronger attenuation of seismic wave amplitudes with distance on Mars. A third possibility is that artificial impacts on the lunar surface represent a better analogue for the seismic response of small impacts on Mars than those that occur into terrestrial soils.

The upper bound on the peak P-wave amplitude may be used to place a joint constraint on the impact seismic efficiency (ks, which is site and impact specific) and the average mantle attenuation (Qμ) along the path from Perseverance’s landing site to InSight.

Because ks and Qμ are entirely independent of each other (the former being related to generation of seismic waves on a local scale, and the latter to their propagation on a global scale), jointly constraining their values in this way is valid.

ks is particularly poorly constrained, due to its high sensitivity to local conditions and the lack of relevant in situ measurements18. All estimates for Mars thus far have therefore used modelling, simulation or material analogues to estimate its value, and no in situ measurements other than those in this paper exist.

Qμ and Qκ are the two quality factors used to describe viscoelastic (intrinsic/inelastic) attenuation properties within the solid part of the planet. The former is associated with shear properties, and the latter with bulk properties.

For typical Martian mantle rheologies, QμQκ, hence Qκ has little influence on P-wave amplitudes. The P-wave attenuation QP can then be approximated as $${Q}_{\mathrm{P}}=\frac{9}{4}{Q}_{\mu }$$.

Tidal observations suggest that Qμ does not vary strongly through the mantle19, so we assume that Qμ is a reasonable descriptor of the average attenuation along the source–receiver path (Methods).

We do not treat the crust separately to the mantle, as the P-wave propagates almost entirely within the latter and previous studies show comparably negligible crustal attenuation15,20. To relate our observed upper bound on the P-wave amplitude to Qμ and ks, we first estimate the seismic moment associated with the CBMD impact using the following empirically derived relationship from ref. 21:

$${M}_{0}=\frac{{({k}_{\mathrm{s}}{E}_{k})}^{0.81}}{4.8\times 1{0}^{-9}}$$
(1)

where Ek is the impactor kinetic energy (in this case, 1.1 GJ). Note that the separation between the CBMDs in space and time at impact (~1 km and around 1 s) is large enough that the impact processes occur independently of each other. Ek is thus the kinetic energy of a single CBMD.

As the P wave reduces in amplitude during its propagation through both attenuation and geometric spreading of the wavefront, making an estimate of Qμ requires us to quantify the effects of the latter.

To do this, we undertake full-waveform seismic simulations using the AxiSEM method22 in a purely elastic (non-attenuating) medium. Thus, the only energy loss in these simulations along the source–receiver path occurs due to the spreading of the wavefront. The effects of attenuation using an average Qμ may then be applied as a post-simulation correction (Methods).

Now, the values of ks and Qμ may be independently varied (using equations (1) and (3), respectively) to determine their joint effect on the amplitude recorded by InSight.

Figure 4 shows joint constraints that may be placed on ks for this impact scenario and Qμ: as increasing the value of either parameter leads to larger predicted amplitudes, these are co-constrained such that the resultant P-wave amplitude does not exceed our detection threshold.

The quality factor has previously been determined to lie in the range 300–1,000, with the lower bound derived from tidal observations19 and the upper from observations of the spectra of marsquakes20,23. Thus, we constrain the maximum value of ks to be 3%, corresponding to the rightmost corner of the green zone in Fig. 4.

This upper limit on ks is compatible with experimental (terrestrial and lunar) and simulated (terrestrial, lunar and Martian) measurements, where ks ranges from 10−6 (in porous sand/regolith) to 10−3 (in stronger, non-porous materials)5,11,17,24,25. Values up to 2–3% have been observed in underground nuclear explosions in stronger target materials26.

Figure 1 shows one of the impact craters. The surrounding morphology is representative of this region of Mars, and consists of aeolian bedforms and unconsolidated/poorly consolidated regolith. The thermal inertia of the surface at the impact location is ~250 J m−2 s−1/2 K−1 (ref. 27), indicative of a dominantly sandy surface. Although a quantitative relationship between ks and target properties has yet to be derived, our upper bound on ks is consistent with a surface material of this type.

The true seismic efficiency is likely to be lower than the maximum that we derived. Nonetheless, this does still demonstrate a practical method through which it may be constrained, and is notable that such a constraint has been derived on Mars. From this, we may draw the robust conclusion that the conversion of kinetic energy into seismic energy on Mars is no more efficient than the most efficient such terrestrial coupling.

We used the non-detection of the seismic waves from the impact of Perseverance’s CBMDs to show that the total impactor momentum is a poor predictor of amplitude at this distance and impact angle, if a terrestrial-based scaling is assumed. In this case, the lunar-based scaling or a relationship based on impactor energy may be more appropriate. This result could also indicate that effects of attenuation on impact-generated seismic waves are stronger than previously estimated.

We also used the non-detection to constrain the impact seismic efficiency to be less than 3%, which is compatible with geological analysis of the impact site, and commensurate with previous estimates, which used modelling or proxies in place of in situ data.

The methodology presented here provides a basis for using seismic (non-) detection of artificial impacts to infer subsurface properties, and could in future be applied during geophysical missions to any of the Solar System’s icy or rocky bodies.

## Methods

We use an interior velocity and density model called ‘TAYAK’, which combines geochemical data with geodetic constraints28,29. This was chosen on the basis of its good fit to other marsquake data30. The source is represented as an explosion just below the surface, as per ref. 18.

Simulations are conducted using the spectral element solver AxiSEM22 in combination with Instaseis31, with a dominant source period of 1 s, and with attenuation switched off. This allows us to account for amplitude decreases due to the geometric spreading of the wavefront.

Once the amplitude in the non-attenuating case A0 (where A0 = A0(M0)) has been found, we account for the effects of attenuation, assuming an effective QP,eff that averages over the propagation path S:

$${Q}_{{{{\rm{P,eff}}}}}^{-1}={\int}_{S}{Q}_{{{{\rm{P}}}}}^{-1}(s)\,{{{\rm{d}}}}s.$$
(2)

The amplitude in a frequency band between f1 and f2 (here 0.2 and 0.9 Hz) is estimated through application of the following equation:

$$A({Q}_{{{{\rm{P,eff}}}}},{M}_{0})={A}_{0}({M}_{0})\frac{\int\nolimits_{{f}_{1}}^{{f}_{2}}\exp \left(-\frac{tf}{2{Q}_{{{{\rm{P,eff}}}}}}\right){{{\rm{d}}}}f}{{f}_{2}-{f}_{1}}$$
(3)

where A is the amplitude at InSight. Note that QP = 9/4Qμ, assuming a Poisson solid with a standard acoustic speed to shear speed ratio vp/vs of $$\sqrt{3}$$. t = 420 s is the predicted travel time of a P wave. Q is assumed to be frequency independent.

Combining equations (3), as derived above, and (1) allows us to determine which combinations of ks and QP,eff (and hence ks and Qμ) produce a permissible A at InSight’s position, that is, one below the detection threshold.